Abstract

We study the dynamics of two vertical-cavity surface-emitting lasers (VCSELs) mutually coupled such that the natural lasing polarization of each laser is rotated by 90 degrees and then is injected into the other laser. Simulations based on the spin-flip model show transient square-wave polarization switchings before a stationary state is reached. The influence of various model parameters on the duration of the stochastic transient time and on the lasers’ dynamics in the stationary state is investigated.

Figures (8)

Linear stability of the x and y polarized states of the solitary lasers in the parameter space (birefringence, injection current). In the red region only the x polarization is stable, in the blue region, only the y polarization is stable, in the white region, both polarizations are stable and in the green region, neither polarization is stable. The model parameters are: k = 300 ns−1, γn = 2 ns−1, γs = 50 ns−1, γa = 0.4 ns−1 and α = 3. The black circle and square indicate the parameters used for Figs. 3(a) and (b) respectively.

Bifurcation diagram for increasing coupling strength. The analytically calculated pure mode solution (black dots) is plotted together with the numerical solution (the extreme values of the oscillations of the x intensity of one laser, I1x in red, and the extreme values of the oscillations of the y intensity of the other laser, I2y in blue). In (a), (b) the coupling is x → y, in (c), (d) the coupling is y → x. The parameters are μ = 2, γp = 60 rad/ns (a), (b), γp = 4 rad/ns (c), (d), other parameters are as indicated in the text.

Transient dynamics towards the “pure-mode” steady-state in which the lasers emit cw orthogonal polarizations. The intensities of the x and y polarizations of the two lasers are plotted vs. time (x red line; y blue line, the intensities were averaged to simulate the finite experimental detection bandwidth). Left panels: the coupling is x → y and the parameters are μ = 2.5, γp = 60 rad/ns, η = 60 ns−1; right panels: y → x, μ = 1.7, γp = 4 rad/ns, η = 80 ns−1, other parameters as indicated in the text. In both cases after a transient time laser 2 (bottom row) acts as “master laser”, emitting the natural polarization of the stand alone laser (x in the left panels and y in the right panels), while laser 1 (top row) is the “injected laser”, emitting the orthogonal polarization.

Left panels: Dynamics of the coupled lasers with x → y coupling, μ = 3.5, other parameters as in the left panels of Fig. 3. After the transient laser 1 (top row) is the “master laser” displaying sustained oscillations of the two polarizations (“solitary laser solution”) and laser 2 (bottom row) is the “injected laser” emitting the y polarization with the same oscillation as the master. Right panels: Dynamics of the coupled lasers with weaker coupling strength and y → x coupling. After the transient laser 2 (bottom row) is the “injected laser” displaying sustained oscillations of the x polarization and laser 1 (top row) is the “master laser” emitting the y polarization with cw output (μ = 2, γp = 4 rad/ns, η = 50 ns−1).